1. Field of the Invention
The present invention relates generally to a method for reconstructing an image and an X-ray CT system, and particularly to a method of reconstructing an image and an X-ray CT system, in which the motion artifacts are reduced and the resolution is high.
2. Description of Related Art
There are various algorithms in the image reconstructing process in the X-ray computed tomography (CT), and the most commonly used algorithm at present is a back projection method. According to the back projection method, fuzziness of the image caused by the back projection process is controlled by applying high-frequency components emphasizing filtration to projection data. The back projection method includes the filtered back projection method performed through multiplying by a filter function in the frequency space and the convolution back projection method performed by the convolution process in the real space.
The filter function used in the above-described back projection method is referred to a reconstructing filter, and the Ramachandran filter and the Shepp & Logan filter as shown in FIG. 4 are normally used.
FIG. 5 is a flow chart showing the conventional process of the filtered back projection method. As shown in FIG. 5, preprocessing, which includes sensitivity corrections for uneven detector cell sensitivities and gains, intensity corrections for variations in X-ray beam, beam hardening corrections, scattered ray corrections, conversion of the data to logarithmic form and the like, is applied to the acquired projection data (Step S10), thereafter, fuzziness of the back projection is corrected in advance by a filtering process (Step S13), and a tomographic image is obtained by a back projection process (Step S14). Further, there may be a case where an image filter is applied to the tomographic image as an after-processing to thereby obtain a final image (Step S15). The image characteristics of the tomographic image obtained as described above rely upon the frequency characteristics of the reconstruction filter, so that, in the X-ray CT system, there are provided various types of filter functions suitable for the respective scanned portions.
However, the spatial resolution in the X-ray CT system is governed by the cell interval and aperture of the detector, and the resolution more than that has been difficult to realize theoretically. Thus, the spatial resolution determined by the cell interval has heretofore been bettered by the improvements in the acquiring method and algorithm.
The conventional high resolution algorithm will hereunder be described. One of the important techniques is a method, in which the redundancy of a fan beam CT scanning is skillfully utilized, i.e., a method, in which acquiring is performed by a 1/4 offset detector which is shifted from a straight line connecting an X-ray tube to the center of rotation by 1/4 of the cell interval, so that a sample position of data opposed thereto through 180.degree. in the direction of channel is shifted by 1/2 pitch of the cell interval as compared with the initial position.
That is, as shown in FIG. 6 (A), when a fan beam angle is .+-..alpha. and a projection angle is .beta., the opposition data of a fan beam projection A at a certain angle (projection angle .beta.) is represented by a straight line B. The opposition data at a certain channel position ai are associated with the same black ball on the straight line B, and similarly, indicate the data of two white balls which are opposed to each other.
Furthermore, as shown in FIG. 6 (B), in a case of performing the scanning by use of a 1/4 offset detector, when the opposition data of the above-described channel position .alpha..sub.i are considered, the position of -.alpha..sub.i falls under the cell border of the detector. These relations are true of all of the channel positions. Accordingly, the same result is obtained by sampling in the direction of a at the 1/2 pitch of the cell interval of the 1/4 offset detector.
Another of the important techniques is that the precision data, in which the cell interval of the 1/4 offset detector is made smaller, is calculated from the acquired data by calculation (oversampling), and a large bandwidth process is applied in the process thereafter.
It is most effective when these two techniques are used simultaneously. That is, this is the method, in which the data positioned between the detecting cells are calculated from the opposition data obtained by the offset acquiring, and the thus obtained result is processed by the large bandwidth process.
When it is intended to calculate the opposition interpolation data of the fan beam projection A at a certain angle (projection angle .beta.), if the cell interval of the 1/4 offset detector is .DELTA..alpha., then the opposition interpolation data coming between P(.alpha..sub.i, .beta.) and P(.alpha..sub.i+1, .beta.) as shown in FIG. 7 are shifted by .DELTA..alpha./2, so that P(.alpha..sub.i +.DELTA..alpha./2, .beta.) is obtained. Accordingly, the side of the opposition data represented by -(.alpha..sub.i +.DELTA..alpha./2), which is just at the cell center of the 1/4 offset detector and corresponds to the sample position in the direction of .alpha..
Actually, correspondence with the sample position in the direction .beta. rarely takes place, so that the opposition data can be calculated by the interpolation process in the direction of .beta.. This process is carried out over all of the channels, and, as shown in FIG. 8, the opposition interpolation data (high resolution data) P of 1/2 pitch of the cell interval of the 1/4 offset detector can be obtained from 0.degree. data P1 and 180.degree. data P2. When the 1/4 offset detector is used as described above, the opposition interpolation data P can be calculated without the interpolation process in the direction of channel, which is important for the resolving power, so that it becomes more effective.
Here, this method is referred to an opposed beam interpolation method. It is known that the spatial resolution can be improved by 25% effectively by the opposed beam interpolation method. FIG. 9 is a flow chart showing the high resolution process in a case of a fan beam direct back projection. As compared with the flow chart shown in FIG. 5, the above-described opposed beam interpolation process (Step S12) is added. Furthermore, FIG. 10 is a flow chart showing the high resolution process in a case of a parallel beam arrangement back projection. As compared with the flow chart shown in FIG. 5, a parallel beam transformation process (Step S11) and the opposed beam interpolation process (Step S12) are added.
However, the high resolution image can be obtained by the opposed beam interpolation process, but, the data opposed to each other through 180.degree. have a shift (phase difference) of about 1/2 scan time. Thus, due to the movements of body and internal organs such as heart beat, respiration and peristaltic movements of bowels, the opposed data may not correspond with the data which are naturally obtained. Furthermore, in the actual scanning, the acquiring is one, in which an area having the spreading toward the detecting cells from the focus is scanned, so that it is difficult to achieve an accurate correspondence. Particularly, in a cross-section where there are small bones as in a head, there may occur an offset portion due to the contradiction between the both. Further, in the most commonly used filtered back projection method among the image reconstruction processes of the X-ray CT system, errors between both are emphasized for applying the high-frequency components emphasizing type filter, and on the reconstructed image, there may take place the streak-shaped artifacts and moire patterns. Furthermore, a shift in position may take place in the focus of an X-ray source due to the change in temperature, and also there may be cases where similar streak-shaped artifacts and moire patterns take place due to the distortions caused by the instrumentation geometry.
On the other hand, in order to control the partial volume effect and to obtain highly accurate data, the scanning may be performed by use of thin slices. In this case, since the efficiency of utilization of X-rays is lowered and image noises are greatly increased, such problems are presented that it is not suitable for observing the lesion having no difference in contrast and, when the high resolution algorithm is applied, the image noises are particularly emphasized.